STABLE ULRICH BUNDLES

2012 ◽  
Vol 23 (08) ◽  
pp. 1250083 ◽  
Author(s):  
MARTA CASANELLAS ◽  
ROBIN HARTSHORNE ◽  
FLORIAN GEISS ◽  
FRANK-OLAF SCHREYER
Keyword(s):  
Vector Bundles ◽  
Sufficient Conditions ◽  
Algebraic Varieties ◽  
Stable Bundles ◽  
Cubic Surfaces ◽  
Number Of Generators ◽  
Class D ◽  
First Chern Class ◽  
Necessary And Sufficient ◽  
Acm Bundles

The existence of stable ACM vector bundles of high rank on algebraic varieties is a challenging problem. In this paper, we study stable Ulrich bundles (that is, stable ACM bundles whose corresponding module has the maximum number of generators) on nonsingular cubic surfaces X ⊂ ℙ3. We give necessary and sufficient conditions on the first Chern class D for the existence of stable Ulrich bundles on X of rank r and c1 = D. When such bundles exist, we prove that the corresponding moduli space of stable bundles is smooth and irreducible of dimension D2 - 2r2 + 1 and consists entirely of stable Ulrich bundles (see Theorem 1.1). We are also able to prove the existence of stable Ulrich bundles of any rank on nonsingular cubic threefolds in ℙ4, and we show that the restriction map from bundles on the threefold to bundles on the surface is generically étale and dominant.

scholarly journals Moduli spaces of vector bundles over ruled surfaces

1999 ◽  
Vol 154 ◽  
pp. 111-122 ◽  
Author(s):  
Marian Aprodu ◽  
Vasile Brînzănescu
Keyword(s):  
Line Bundle ◽  
Moduli Spaces ◽  
Vector Bundles ◽  
Ample Line Bundle ◽  
Sufficient Conditions ◽  
Ruled Surface ◽  
Stable Bundles ◽  
Isomorphism Classes ◽  
Numerical Invariants ◽  
Necessary And Sufficient

AbstractWe study moduli spaces M(c1, c2, d, r) of isomorphism classes of algebraic 2-vector bundles with fixed numerical invariants c1, c2, d, r over a ruled surface. These moduli spaces are independent of any ample line bundle on the surface. The main result gives necessary and sufficient conditions for the non-emptiness of the space M(c1, c2, d, r) and we apply this result to the moduli spaces ML(c1, c2) of stable bundles, where L is an ample line bundle on the ruled surface.

Quantum Kostka and the rank one problem for 𝔰𝔩2m

2019 ◽  
Vol 19 (1) ◽  
pp. 71-88
Author(s):  
Natalie L. F. Hobson
Keyword(s):  
Vector Bundles ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Chern Classes ◽  
Finitely Generated ◽  
Conformal Blocks ◽  
Rank One ◽  
Necessary And Sufficient ◽  
Nef Cone

Abstract We give necessary and sufficient conditions to specify vector bundles of conformal blocks for 𝔰𝔩2m with rectangular weights which have ranks 0, 1, and larger than 1. We show that the first Chern classes of such rank one bundles determine a finitely generated subcone of the nef cone.

QUASIANALYTIC FUNCTION CLASSES AND THE COMPLEX-TIME DIFFUSION GROUP - I

1995 ◽  
Vol 05 (02) ◽  
pp. 167-190 ◽  
Author(s):  
A. GULISASHVILI ◽  
G.H. SANDRI
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Complex Time ◽  
Function Classes ◽  
Group I ◽  
Class D ◽  
Rate Of Decay ◽  
Necessary And Sufficient

In this paper necessary and sufficient conditions are given for quasianalytic function classes D({Mk}) and the corresponding classes of distributions D′({Mk}) to be invariant with respect to the diffusion group Ut where −∞<t<∞. In addition, the properties of hyperdistributions [Formula: see text] are studied, where δ0 denotes the δ-function at 0. It is shown that hyperdistributions Γ from the class D′({Mk}) are completely characterized by the rate of decay of the moments μk(Γ) = Γ(xk), k≥0.

scholarly journals Vector bundles over (8k + 5)-dimensional manifolds

1989 ◽  
Vol 111 (1-2) ◽  
pp. 183-197 ◽  
Author(s):  
Tze-Beng Ng
Keyword(s):  
Tangent Bundle ◽  
Smooth Manifold ◽  
Vector Bundles ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Necessary And Sufficient

Suppose that M is a closed, connected and smooth manifold of dimension n = 8k + 5, with k ≧1. Let η be an n-plane bundle over M. Under suitable conditions on M, we derive necessary and sufficient conditions for the span of η to be ≧j, j = 5 or 6. We then apply the results to the tangent bundle of M. In particular, we prove a conjecture of E. Thomas, namely, if M is 3-connected mod 2, then span M ≧ 5 if, and only if, χ2(M) = 0. We prove that if also w8k(M) = 0, then span M≧6. We also derive some immersion theorems for M.

The extinction time of a general birth and death process with catastrophes

1986 ◽  
Vol 23 (04) ◽  
pp. 851-858 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Laplace Transform ◽  
Size Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Death Process ◽  
Extinction Time ◽  
Birth And Death Process ◽  
Different Types ◽  
The Laplace Transform ◽  
Necessary And Sufficient

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj&gt; 0 for eachj&gt; 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.

Budgeting in Socio-economic Development Strategies (Raising a Problem)

2008 ◽  
pp. 134-151
Author(s):  
A. Shastitko ◽  
M. Ovchinnikov
Keyword(s):  
Economic Policy ◽  
Economic Development ◽  
Social Change ◽  
Eastern Europe ◽  
Statistical Data ◽  
Sufficient Conditions ◽  
Transitional Period ◽  
Socio Economic Development ◽  
Necessary And Sufficient ◽  
Economic Development Strategies

The article proposes an approach to the analysis of social change and contributes to the clarification of concepts of economic policy. It deals in particular with the notion of "change of system". The author considers positive and normative aspects of the analysis of capitalist and socialist systems. The necessary and sufficient conditions for the system to be changed are introduced, their fulfillment is discussed drawing upon the historical and statistical data. The article describes both economic and political peculiarities of the transitional period in different countries, especially in Eastern Europe.

Inventory optimization considering the vehicle capacity and specifics of cash flows at rental storage sites

2020 ◽  
pp. 77-90
Author(s):  
V.D. Gerami ◽  
I.G. Shidlovskii
Keyword(s):  
Supply Chain ◽  
Inventory Management ◽  
Sufficient Conditions ◽  
Cash Flows ◽  
Management Systems ◽  
Cargo Capacity ◽  
Special Modification ◽  
The Cost ◽  
Necessary And Sufficient ◽  
Vehicle Capacity

The article presents a special modification of the EOQ formula and its application to the accounting of the cargo capacity factor for the relevant procedures for optimizing deliveries when renting storage facilities. The specified development will allow managers to take into account the following process specifics in the format of a simulated supply chain when managing inventory. First of all, it will allow considering the most important factor of cargo capacity when optimizing stocks. Moreover, this formula will make it possible to find the optimal strategy for the supply of goods if, also, it is necessary to take into account the combined effect of several factors necessary for practice, which will undoubtedly affect decision-making procedures. Here we are talking about the need for additional consideration of the following essential attributes of the simulated cash flow of the supply chain: 1) time value of money; 2) deferral of payment of the cost of the order; 3) pre-agreed allowable delays in the receipt of revenue from goods sold. Developed analysis and optimization procedures have been implemented to models of this type that are interesting and important for a business. This — inventory management systems, the format of which is related to the special concept of efficient supply. We are talking about models where the presence of the specified delays for the outgoing cash flows allows you to pay for the order and the corresponding costs of the supply chain from the corresponding revenue on the re-order interval. Accordingly, the necessary and sufficient conditions are established based on which managers will be able to identify models of the specified type. The purpose of the article is to draw the attention of managers to real opportunities to improve the efficiency of inventory management systems by taking into account these factors for a simulated supply chain.

Nonlinear boundary-value problems for degenerate differential-algebraic systems

2020 ◽  
Vol 17 (3) ◽  
pp. 313-324
Author(s):  
Sergii Chuiko ◽  
Ol'ga Nesmelova
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Algebraic System ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Weakly Nonlinear ◽  
Differential Algebraic System ◽  
Linear Differential ◽  
Necessary And Sufficient

The study of the differential-algebraic boundary value problems, traditional for the Kiev school of nonlinear oscillations, founded by academicians M.M. Krylov, M.M. Bogolyubov, Yu.A. Mitropolsky and A.M. Samoilenko. It was founded in the 19th century in the works of G. Kirchhoff and K. Weierstrass and developed in the 20th century by M.M. Luzin, F.R. Gantmacher, A.M. Tikhonov, A. Rutkas, Yu.D. Shlapac, S.L. Campbell, L.R. Petzold, Yu.E. Boyarintsev, V.F. Chistyakov, A.M. Samoilenko, O.A. Boichuk, V.P. Yacovets, C.W. Gear and others. In the works of S.L. Campbell, L.R. Petzold, Yu.E. Boyarintsev, V.F. Chistyakov, A.M. Samoilenko and V.P. Yakovets were obtained sufficient conditions for the reducibility of the linear differential-algebraic system to the central canonical form and the structure of the general solution of the degenerate linear system was obtained. Assuming that the conditions for the reducibility of the linear differential-algebraic system to the central canonical form were satisfied, O.A.~Boichuk obtained the necessary and sufficient conditions for the solvability of the linear Noetherian differential-algebraic boundary value problem and constructed a generalized Green operator of this problem. Based on this, later O.A. Boichuk and O.O. Pokutnyi obtained the necessary and sufficient conditions for the solvability of the weakly nonlinear differential algebraic boundary value problem, the linear part of which is a Noetherian differential algebraic boundary value problem. Thus, out of the scope of the research, the cases of dependence of the desired solution on an arbitrary continuous function were left, which are typical for the linear differential-algebraic system. Our article is devoted to the study of just such a case. The article uses the original necessary and sufficient conditions for the solvability of the linear Noetherian differential-algebraic boundary value problem and the construction of the generalized Green operator of this problem, constructed by S.M. Chuiko. Based on this, necessary and sufficient conditions for the solvability of the weakly nonlinear differential-algebraic boundary value problem were obtained. A typical feature of the obtained necessary and sufficient conditions for the solvability of the linear and weakly nonlinear differential-algebraic boundary-value problem is its dependence on the means of fixing of the arbitrary continuous function. An improved classification and a convergent iterative scheme for finding approximations to the solutions of weakly nonlinear differential algebraic boundary value problems was constructed in the article.

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